In the last three decades, condensed matter physicists have discovered a wonderland of exotic new phases of matter: emergent, collective states of interacting particles that are nothing like the solids, liquids and gases of common experience.

Now, research groups at Microsoft and elsewhere are racing to encode quantum information in the braids and loops of some of these phases for the purpose of developing a quantum computer. Meanwhile, condensed matter theorists have recently made major strides in understanding the pattern behind the different collective behaviors that can arise, with the goal of enumerating and classifying all possible phases of matter. If a complete classification is achieved, it would not only account for all phases seen in nature so far, but also potentially point the way toward new materials and technologies.

The article includes discussion of the toric code, a phase theoretically constructed by Alexei Kitaev. Former Preskill group Graduate Student Jeongwan Haah’s development of the “Haah Code” in 2011 and his additional more recent work when he and collaborators at MIT discovered “fracton models” related to the Haah code.

Xie Chen’s interest has developed into her work on fractons “The Haah phase is opening the door to many more exotic things. It’s an indication about how little we know about 3-D and higher dimensions.”